### Abstract

The QED vacuum polarization in external monochromatic plane-wave electromagnetic fields is calculated with spatial and temporal variations of the external fields being taken into account. We develop a perturbation theory to calculate the induced electromagnetic current that appears in the Maxwell equations, based on Schwinger's proper time method, and combine it with the so-called gradient expansion to handle the variation of external fields perturbatively. The crossed field, i.e., the long wavelength limit of the electromagnetic wave, is first considered. The eigenmodes and the refractive indices, as the eigenvalues associated with the eigenmodes, are computed numerically for the probe photon propagating in some particular directions. In so doing, no limitation is imposed on the field strength and the photon energy, unlike previous studies. It is shown that the real part of the refractive index becomes less than unity for strong fields, a phenomenon that has been known to occur for high-energy probe photons. We then evaluate numerically the lowest-order corrections to the crossed field resulting from the field variations in space and time. It is demonstrated that the corrections occur mainly in the imaginary part of the refractive index.

Original language | English |
---|---|

Article number | 033B04 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2018 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2018 Mar 1 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Vacuum polarization and photon propagation in an electromagnetic plane wave.** / Yatabe, Akihiro; Yamada, Shoichi.

Research output: Contribution to journal › Article

*Progress of Theoretical and Experimental Physics*, vol. 2018, no. 3, 033B04. https://doi.org/10.1093/ptep/pty009

}

TY - JOUR

T1 - Vacuum polarization and photon propagation in an electromagnetic plane wave

AU - Yatabe, Akihiro

AU - Yamada, Shoichi

PY - 2018/3/1

Y1 - 2018/3/1

N2 - The QED vacuum polarization in external monochromatic plane-wave electromagnetic fields is calculated with spatial and temporal variations of the external fields being taken into account. We develop a perturbation theory to calculate the induced electromagnetic current that appears in the Maxwell equations, based on Schwinger's proper time method, and combine it with the so-called gradient expansion to handle the variation of external fields perturbatively. The crossed field, i.e., the long wavelength limit of the electromagnetic wave, is first considered. The eigenmodes and the refractive indices, as the eigenvalues associated with the eigenmodes, are computed numerically for the probe photon propagating in some particular directions. In so doing, no limitation is imposed on the field strength and the photon energy, unlike previous studies. It is shown that the real part of the refractive index becomes less than unity for strong fields, a phenomenon that has been known to occur for high-energy probe photons. We then evaluate numerically the lowest-order corrections to the crossed field resulting from the field variations in space and time. It is demonstrated that the corrections occur mainly in the imaginary part of the refractive index.

AB - The QED vacuum polarization in external monochromatic plane-wave electromagnetic fields is calculated with spatial and temporal variations of the external fields being taken into account. We develop a perturbation theory to calculate the induced electromagnetic current that appears in the Maxwell equations, based on Schwinger's proper time method, and combine it with the so-called gradient expansion to handle the variation of external fields perturbatively. The crossed field, i.e., the long wavelength limit of the electromagnetic wave, is first considered. The eigenmodes and the refractive indices, as the eigenvalues associated with the eigenmodes, are computed numerically for the probe photon propagating in some particular directions. In so doing, no limitation is imposed on the field strength and the photon energy, unlike previous studies. It is shown that the real part of the refractive index becomes less than unity for strong fields, a phenomenon that has been known to occur for high-energy probe photons. We then evaluate numerically the lowest-order corrections to the crossed field resulting from the field variations in space and time. It is demonstrated that the corrections occur mainly in the imaginary part of the refractive index.

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U2 - 10.1093/ptep/pty009

DO - 10.1093/ptep/pty009

M3 - Article

VL - 2018

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 3

M1 - 033B04

ER -